Portion `AB` of the wedge shown in figure is rough and `BC` is smooth. A solid cylinder rolld without slipping from `A` to `B`. Find the ratio of translational kinetic energy to rotational kinetic energy, when the cylinder reaches point `C`.
.

Options

A. `3//5`
B. `5`
C. `7//5`
D. `8//3`

Answer

B

Explanation

`K=betaK_(T)`
or `K_(T)+K_(R)=betaK_(T)`
`K_(R)=(beta-1)K_(T)impliesK_(R)=1/2K_(T)`
At point B: `K_(T)+K_(R)=mgxxh`
`:.K_(R)=(mgh)/3`
At point C: `K_(T)+(mgh)/3=mgxx2h`
`K_(T)=(5mgh)/3`
`:.(K_(T))/(K_(R))=5`